<main>
  
  <div>
     This is a block-level element with an unknown fixed height, centered vertically within my parent element.
  </div>
  
</main>

body {
  background: #40BDB7;
  font-size: 80%;
}

main {
  background: white;
  height: 300px;
  margin: 20px;
  width: 300px;
  position: relative;
  resize: vertical;
  overflow: auto;
  border-radius: 5px;
}

main div {
  position: absolute;
  top: 50%;
  left: 20px;
  right: 20px;
  background: black;
  color: white;
  padding: 20px;
  transform: translateY(-50%);
  resize: vertical;
  overflow: auto;
}